递归最小二乘自适应滤波器在平稳和非平稳环境中跟踪与收敛特性的研究

Study of Tracking and Converging of Recursive Least Squarrs filters in Stationary and Nonstationary Environments

近些年提出并研究的递归最小二乘(RLS)滤波是自适应信号处理领域中的一项新技术,本文研究了其用于平稳和非平稳时变环境中的跟踪与收敛等特性,导出了更为一般的暂态“滞后误差”公式,给出了一种判别能否收敛的方法。本文还给出了一个额外权向量总误差公式和额外均方误差公式,根据它讨论了RLS算法启动段的初始收敛情况,并认为[4]中有关这方面的分析需要改进。对于所得的主要结论,文中采用计算机模拟进行了验证,理论值与模拟结果吻合良好。这些结论在使用递归最小二乘算法时合理地选取各种参数,具有重要的指导意义。

Recently raised and developed RLS filtering is a new techniqeuin adaptive processing, and it is on the forefront to study the behavior of its tracking and converging in stationary and nonstationary environmonts, In the paper, this interest study is carried out .General transiant' Lag Error' formulae is derived, A method to judge the convergence is given. Additional weight vector error and MSE formula are presented. Using them, the initial convergence of RLS algorithms is discussed. It is pointed out in the paper that the relevnt analysis in (4) needs adapting. The main results obtained in this paper are verified by computer simulation.They are useful and very important to properly choose the paraneters of the RLS filte is in various applications.